David Miliband, the foreign secretary, and Ed Balls, the schools secretary, are poised to declare their candidacy for the Labour leadership once negotiations with the Liberal Democrats are completed.

Amid delicate talks with the Lib Dems over a possible coalition, it was agreed at last night's cabinet meeting that no bids would be launched until the talks had ended. A ministerial aide said: "You can't have anyone breaking cover."

Miliband said the agreement meant no potential candidate would launch their leadership campaign before coalition talks conclude. "I intend to abide by those rules decided at cabinet today," he said.

But Miliband, who emerged as favourite with the bookmakers last night, and Balls are certain to run. The energy and climate change secretary, Ed Miliband, and the health secretary, Andy Burnham, are also taking soundings from colleagues about their chances if they run.

Odds are also being offered against the veteran ministers Alistair Darling, the chancellor, Harriet Harman, Labour's deputy leader and Alan Johnson, the home secretary, though they have, to differing extents, ruled themselves out of the leadership race. The backbencher Jon Cruddas, MP for Dagenham and Rainham, is expected to be the main candidate on the left of the party.

The contest, which is expected to last through the summer, would be the first to feature brothers if Ed Miliband, the younger sibling, chooses to enter the race. There were no denials after a newspaper report yesterday that he had told his mother he was planning to stand.

Any other contenders were keeping quiet last night, perhaps hoping to get a part of the negotiations with the Lib Dems over the possible coalition under their belts before a leadership war began.

There is consensus across the party that any leadership campaign must be as swift as possible. Brown said in his resignation speech that a new leader should be in place by the party conference in the autumn.

David Miliband and Balls are understood to already have leadership race strategies in place, with a campaign team on call. The former work and pensions secretary James Purnell, who stood down as an MP at the last election, is likely to lead the foreign secretary's campaign, with suggestions that he could become chief of staff if he wins.

Miliband is keen not to take any risks in his bid, after the damaging episode two years ago when he signalled he was ready to challenge Brown for the leadership but made a U-turn at the 11th hour.

Balls has previously said he would stand, but last night was busy fulfilling his role in Labour's negotiating team, and was not making any comments on his possible candidacy. The schools secretary has developed a public persona and is well-known, but the key challenge he faces is rehabilitating his image as an abrasive "class warrior". Last week he began that process in a New Statesman interview in which he said: "I'm caricatured as a tribalist. That's garbage. It's not that I'm tribal. It's just that I'm not a Tory. I'm Labour. I believe in Labour values."

He also distanced himself from the negative briefing associated with his close allies Charlie Whelan, political director of the powerful Unite union, and Damian McBride, the former No 10 spin doctor, claiming he was much more a victim of off-the-record briefings than a perpetrator.

Ed Miliband could be thought of as a dark horse. Relatively unknown outside Westminster, he has strong support within the cabinet – he co-ordinated the Labour manifesto – and the unions. Supporters say he is a strong media performer and has a personal touch his brother lacks. Like Balls, he has experience at the Treasury and has union links. A successor to Brown will have to take the reins knowing they could be the second party leader to become prime minister having not led the party in an election campaign.

A Labour party spokesman said: "Gordon Brown has always felt the most important priorities for the country are securing the recovery and changing our politics for good. Gordon Brown's words were the mark of a man who has always put his country first. The Labour party's national executive committee will meet in the coming days to determine the procedures for a leadership election."

How they pick a new leader

• The national executive committee will hold a conference call today to start the process of defining the rules and setting out a timetable. The committee is chaired by Ann Black, a trade unionist, and includes Gordon Brown and Harriet Harman. It is also likely to meet later to finalise procedures.

• The election is likely to take months rather than weeks. The last comparable process was when Harriet Harman won the deputy leadership in 2007. That took seven weeks. One option is for the contest to culminate at the party's conference in October. Brown said he hoped a new leader would be in place by then. A shorter, seven-week campaign could have a result in early July.

• Candidates need to secure nominations from 12.5% of the parliamentary Labour party – at least 32 MPs each. Brown said he will not back any candidate or play any part in the campaign.

• It involves polling several million people. During the deputy leadership contest, more than 3 million MPs, MEPs, party members and members of affiliated unions and other socialist societies were balloted.

• The electoral college is divided into equal thirds. MPs and MEPs; party members; affiliated organisations. Unions ballot members who pay political levies and divide their votes accordingly. An MP who is a party member and a union member would be entitled to vote three times.

• During the deputy leadership election, the NEC decided to run a "redistributive ballot" which allowed voters to rank candidates. The worst performer was knocked out and their votes transferred to the voter's second preference candidate. A similar system is likely to be used again.